Asocial and antisocial are really quite different, though we (societally) confuse the two words - even a quick Google gives pretty mixed answers. If you aren't playing games for the express purpose of ruining the fun of others, you sound more asocial than antisocial to me. Just throwing that out there in case it happens to be useful.
You're right about the definition of asocial, but in every dictionary I've found, antisocial actually means both. Antisocial behaviour is generally more about harming others, while describing oneself as antisocial is generally just avoiding others.
I'm curious if you're from the UK because when I was there, I noticed a lot more people use antisocial in the context of harming others or society, while in north America we use it more in the avoiding others context.
Ah, fair, and nope I'm US based but I basically have what I've concluded must be an abnormal desire for accuracy and specificity with language. I just prefer and appreciate nuanced, specific meanings. But I'm also well aware that vocabulary and grammatical rules are only ever just guidelines - language is a living thing defined by the people that use it, by the way that they all choose to use it - it's all essentially just this massive consensus with a rich and detailed topology, and I love that part too. So I'm not even very consistent when it comes down to it, lol.